Prof. Ilya Tyomkin
Time and Place:
- Complex numbers. Fields: definition and properties. Examples.
- Systems of Linear equations. Gauss elimination process.
- Matrices and operations on them. Invertible matrices.
- Determinant: definition and properties. Adjoint matrix. Cramer rule.
- Vector spaces and subspaces. Linear spanning and linear dependence. Basis and dimension. Coordinates with respect to a given basis.
- Linear transformations. Kernel and Image. Isomorphism of vector spaces. Matrix of a linear transformation with respect to given bases.
- The space of linear transformations between two vector spaces. Dual space